מצנפת, מגבעת, Letter of Aristeas

A peculiar description regarding the כהן גדול in the Letter of Aristeas or אגרת אריסטיאס at verse 98 (see text)  :

On his breast he wore the oracle of God, as it is called, on which twelve stones, of different kinds, were inset, fastened together with gold, containing the names of the leaders of the tribes, according to their original order, each one flashing forth in an indescribable way 98 its own particular colour. On his head he wore a tiara, as it is called, and upon this in the middle of his forehead an inimitable turban, the royal diadem full of glory with the name of God inscribed in sacred letters on a plate of gold

It sounds like from here the כהן גדול wore both a מגבעת and a מצנפת....